Windowed Green Function MoM for Second-Kind Surface Integral Equation Formulations of Layered Media Electromagnetic Scattering Problems

TL;DR

This paper introduces a high-order convergent, layer Green function-free second-kind surface integral equation method for electromagnetic scattering in layered media, reducing computational domain size with a windowed Green function approach.

Contribution

It develops a novel windowed Green function method combined with a second-kind integral equation that avoids layer Green functions, improving efficiency and accuracy in layered media scattering problems.

Findings

High-order convergence achieved with the windowed Green function method

Method validated against exact solutions and layer Green function-based MoM

Effective for complex structures like plasmonic solar cells and metasurfaces

Abstract

This paper presents a second-kind surface integral equation method for the numerical solution of frequency-domain electromagnetic scattering problems by locally perturbed layered media in three spatial dimensions. Unlike standard approaches, the proposed methodology does not involve the use of layer Green functions. It instead leverages an indirect M\"uller formulation in terms of free-space Green functions that entails integration over the entire unbounded penetrable boundary. The integral equation domain is effectively reduced to a small-area surface by means of the windowed Green function method, which exhibits high-order convergence as the size of the truncated surface increases. The resulting (second-kind) windowed integral equation is then numerically solved by means of the standard Galerkin method of moments (MoM) using RWG basis functions. The methodology is validated by comparison with Mie-series and Sommerfeld-integral exact solutions as well as against a layer Green function-based MoM. Challenging examples including realistic structures relevant to the design of plasmonic solar cells and all-dielectric metasurfaces, demonstrate the applicability, efficiency, and accuracy of the proposed methodology.